The angle between the lines,whose direction cosines $l, m, n$ satisfy the equations $l+m+n=0$ and $2l^2+2m^2-n^2=0$,is (in $^{\circ}$)

If $\ell, m, n$ and $a, b, c$ are direction cosines of two lines, then:

If the lengths of projections of a line of length $l$ over the coordinate axes are $l_1, l_2$ and $l_3$ respectively,then $l_1^2+l_2^2+l_3^2$ is equal to

The vector $\vec{r}$ whose magnitude is $3\sqrt{2}$ units and which makes angles of $\frac{\pi}{4}$ and $\frac{\pi}{2}$ with the positive $y$- and $z$-axes respectively is....

If the direction cosines of two lines are such that $l+m+n=0$ and $l^2+m^2-n^2=0$, then the angle between them is:

$A$ space vector makes the angles $150^{\circ}$ and $60^{\circ}$ with the positive direction of $x$- and $y$-axes. The angle made by the vector with the positive direction of the $z$-axis is (in $^{\circ}$)